Nonlinear Wave-Wave Interactions in the Brain

Abstract

Neural field theory of the corticothalamic system is used to analyze nonlinear wave-wave interactions in sleep and wake states and steady state visual evoked potential responses. The nonlinear power spectrum is analytically calculated by convolving the linear power spectrum with itself and other factors. Analysis shows that strong spectral peaks generate a harmonic at twice the original frequency with peak power proportional to the square of that of the original peak. Periodic sine and square wave stimuli are used to generate steady state visual evoked potential responses and to study stimulus-driven nonlinear corticothalamic dynamic interactions. Dual sine drives are then used to analyze the driven dynamics more clearly, without the complicating effects of a background spectrum. Numerical analysis shows that the nonlinear power spectrum embodies key nonlinear features, including harmonic and subharmonic generation, entrainment of alpha rhythm to periodic stimuli at the drive frequency, sum and difference frequencies due to wave-wave coalescence and decay. Further, the scaling properties of the key phenomena observed in nonlinear interactions are studied, verifying some of the theoretical predictions for these being generated by three-wave processes.